Algorithmic Problems in Groups and Semigroups

This volume contains papers which are based primarily on talks given at an inter­ national conference on Algorithmic Problems in Groups and Semigroups held at the University of Nebraska-Lincoln from May ll-May 16, 1998. The conference coincided with the Centennial Celebration of the Department of Mathematics and Statistics at the University of Nebraska-Lincoln on the occasion of the one hun­ dredth anniversary of the granting of the first Ph.D. by the department. Funding was provided by the US National Science Foundation, the Department of Math­ ematics and Statistics, and the College of Arts and Sciences at the University of Nebraska-Lincoln, through the College's focus program in Discrete, Experimental and Applied Mathematics. The purpose of the conference was to bring together researchers with interests in algorithmic problems in group theory, semigroup theory and computer science. A particularly useful feature of this conference was that it provided a framework for exchange of ideas between the research communities in semigroup theory and group theory, and several of the papers collected here reflect this interac­ tion of ideas. The papers collected in this volume represent a cross section of some of the results and ideas that were discussed in the conference. They reflect a synthesis of overlapping ideas and techniques stimulated by problems concerning finite monoids, finitely presented mono ids, finitely presented groups and free groups.

Syntactic and Global Semigroup Theory: A Synthesis Approach.- Semigroups with Central Idempotents.- Algebraic Geometry over Groups.- Aspects of the Theory of Free Groups.- Polynomial Isoperimetric Inequalities for Richard Thompson’s Groups F, T,and V.- Ordered Monoids and J-Trivial Monoids.- A Remark on Finitely Generated Subgroups of Free Groups.- Homotopy Reduction Systems for Monoid Presentations II:The Guba—Sapir Reduction and Homotopy Modules.- Algorithmic Problems for Finite Groups and Finite Semigroups.- A Survey on the Computational Power of Some Classes of Finite Monoid Presentations.- Rewriting Systems, Finiteness Conditions, and Associated Functions.- Multiparty Communication Complexity of Finite Monoids.- Presentations for Monoids, Their Maximal Subgroups, and Schützenberger Groups.- On the Growth of Relatively Free Semigroups.- When Can One Finite Monoid Simulate Another?.- Computing Closures of Finitely Generated Subgroups of the Free Group.